Q. 428 - Intermediate Algebra

Question

In the following exercises, solve.

$y^2-y-72=0$

Step-by-Step Solution

Answer

Answer is $y=-8,y=9$

Step 1. Given

The quadratic equation is $y^2-y-72=0$

Step 2. Simplify the quadratic equation

$$\begin{gathered} y^2-y-72=0 \\ {y}^2-9y+8y-72=0 \\ y(y-9)+8(y-9)=0 \\ (y-9)(y+8)=0 \end{gathered}$$

So,

$$\begin{gathered} y-9=0 \\ y=9 \end{gathered}$$

and

$$\begin{gathered} y+8=0 \\ y=-8 \end{gathered}$$

Step 3. Check both the values

Put $y=9$ in original equation,

$$\begin{gathered} y^2-y-72=0 \\ {9}^2-9-72=0 \\ 81-9-72=0 \\ 0=0 \end{gathered}$$

True

Now put $y=-8$ in original equation,

$$\begin{gathered} y^2-y-72=0 \\ {(-8)}^2-(-8)-72=0 \\ 64+8-72=0 \\ 0=0 \end{gathered}$$

True

Step 4. Required answer

Answer is $y=-8,y=9$